Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxint = -1u >> 2;
const double eps = 1e-6;
int main() {
  int k;
  cin >> k;
  double n = 1.0;
  while (n * n < k) {
    double m = sqrt(2.0 * k - n * (n + 1.0) + 0.25) - 0.5;
    if (ceil(m) == floor(m)) {
      cout << "YES" << endl;
      return 0;
    }
    n += 1.0;
  }
  cout << "NO" << endl;
  return 0;
}